AP Physics C: Mechanics · Topic 3.4

Topic 3.4: Conservation of Energy

Unit 3: Work, Energy, and Power15-25% of the multiple-choice section

Energy is conserved in all interactions. Whether the energy of a system is constant depends on the system you selected: zero work done on it and no nonconservative interactions inside it means constant mechanical energy. AP Physics C states this topic in exactly the same words as AP Physics 1.

AP Physics: Unit 3 (topics 3.4 Conservation of Energy). Topic 3.4 of the current AP Physics C: Mechanics course and exam description (Unit 3, weighted 15 to 25% of the multiple-choice section at about 12 to 17 class periods). Three learning objectives, more than any other topic in Unit 3, and nine essential knowledge statements with no sub-statements: 3.4.A.1 and .2 on which energies a system can have, 3.4.B.1 to .4 on mechanical energy and the balance of changes, and 3.4.C.1 to .3 on how the choice of system decides whether its energy changes. Boundary statement, quoted whole: AP Physics C: Mechanics expects students to know that mechanical energy can be dissipated as thermal energy or sound by nonconservative forces. Every learning objective sentence and every essential knowledge statement is word for word identical to AP Physics 1's Topic 3.4, and the two boundary statements differ only in the course name, so this page says so plainly rather than manufacturing a difference: the calculus entered upstream, in Topics 3.2 and 3.3, and by Topic 3.4 the terms are already in hand. What does differ sits outside the required content: suggested skills (AP Physics 1 lists 1.A, 2.A, 2.C, 3.C; AP Physics C: Mechanics lists 1.B, 2.A, 2.C, 3.A, 3.C per the Unit at a Glance page), roughly half the class periods for the same five topic titles, and the derivation-first, symbolic-answer form the C free-response section expects. NOTE a CED internal inconsistency recorded on the page: the Unit at a Glance page (printed p.64) gives Topic 3.4's fifth suggested skill as 3.C, while the Topic 3.4 page (printed p.74) prints the badge 3.B beside skill 3.C's wording. Sample-question load: 3.4.B appears in three of the four sample free-response questions (1, 3 and 4), more than any other objective in the course, and in sample multiple-choice questions 1 and 8, both tagged to 3.4.B.2; 3.4.C appears in sample free-response Question 3 only; 3.4.A appears in no sample question.

What Topic 3.4 requires, in full

Topic 3.4 carries three learning objectives, more than any other topic in Unit 3, and nine essential knowledge statements with no sub-statements anywhere.

Objective and statement	What the CED says
3.4.A	Describe the energies present in a system
3.4.A.1	A system composed of only a single object can only have kinetic energy
3.4.A.2	A system that contains objects that interact via conservative forces or that can change its shape reversibly may have both kinetic and potential energies
3.4.B	Describe the behavior of a system using conservation of mechanical energy principles
3.4.B.1	Mechanical energy is the sum of a system's kinetic and potential energies
3.4.B.2	Any change to a type of energy within a system must be balanced by an equivalent change of other types of energies within the system or by a transfer of energy between the system and its surroundings
3.4.B.3	A system may be selected so that the total energy of that system is constant
3.4.B.4	If the total energy of a system changes, that change will be equivalent to the energy transferred into or out of the system
3.4.C	Describe how the selection of a system determines whether the energy of that system changes
3.4.C.1	Energy is conserved in all interactions
3.4.C.2	If the work done on a selected system is zero and there are no nonconservative interactions within the system, the total mechanical energy of the system is constant
3.4.C.3	If the work done on a selected system is nonzero, energy is transferred between the system and the environment

Topic 3.4's boundary statement, quoted whole: "AP Physics C: Mechanics expects students to know that mechanical energy can be dissipated as thermal energy or sound by nonconservative forces."

Suggested skills, with a note. The Unit at a Glance page lists 1.B (create quantitative graphs with appropriate scales and units, including plotting data), 2.A (derive a symbolic expression), 2.C (compare physical quantities between scenarios), 3.A (create experimental procedures appropriate for a given scientific question) and 3.C (justify or support a claim using evidence). The Topic 3.4 page itself prints the same five entries in the same order, but its fifth badge reads 3.B while carrying the wording of skill 3.C. The two pages of the CED disagree on that one badge; the wording is 3.C's on both. This page follows the Unit at a Glance list.

This is the only topic in Unit 3 with three learning objectives; the other four carry one each.

Every statement here is word for word AP Physics 1's

Set the two course and exam descriptions side by side at Topic 3.4 and there is nothing to report. All three learning objective sentences match. All nine essential knowledge statements match, in the same order, under the same numbers. Neither course adds a sub-statement.

The boundary statements differ by the course name and nothing else:

AP Physics C: Mechanics: "AP Physics C: Mechanics expects students to know that mechanical energy can be dissipated as thermal energy or sound by nonconservative forces."
AP Physics 1: "AP Physics 1 expects students to know that mechanical energy can be dissipated as thermal energy or sound by nonconservative forces."

That is the honest finding, and stating it is more useful than manufacturing a difference. Conservation of energy is one of the few places in mechanics where calculus adds nothing to the principle. The statement "energy is conserved in all interactions" is not made sharper by an integral. What the integral changed was upstream, in Topic 3.2 and Topic 3.3, where the calculus-based course gets its $W$ and its $U$ from integrals rather than from formulas. By the time you reach Topic 3.4 the terms are already in hand and the accounting is the same accounting.

So if you are in AP Physics 1, the AP Physics 1 Topic 3.4 page is your page and nothing here contradicts it. The rest of this page is about what the AP Physics C: Mechanics exam does with the same nine statements, which is where the two courses do part.

What actually differs, and it is not the framework

Four differences, all of them outside the required content.

The suggested skills. AP Physics 1 lists 1.A, 2.A, 2.C and 3.C for its Topic 3.4. AP Physics C: Mechanics lists 1.B, 2.A, 2.C, 3.A and 3.C. The calculus-based course swaps qualitative diagrams (1.A) for quantitative graphs with scales and plotted data (1.B) and adds 3.A, create experimental procedures. Both keep 2.A, derive a symbolic expression, which is the most heavily weighted skill on the AP Physics C: Mechanics multiple-choice section at 25 to 30%.

The time. AP Physics 1's Unit 3 is about 22 to 27 class periods; AP Physics C: Mechanics' is about 12 to 17. Same five topic titles, roughly half the classroom time.

The weighting. AP Physics 1's Unit 3 is 18 to 23% of its multiple-choice section. AP Physics C: Mechanics' Unit 3 is 15 to 25%, a range whose ceiling ties Unit 2's for the highest in the course and whose 10-point width ties Unit 4's for the widest.

The expected form of an answer. This is the one that costs marks. The AP Physics C: Mechanics free-response section is half the exam: four questions in 95 minutes, one each of Mathematical Routines, Translation Between Representations, Experimental Design and Analysis, and Qualitative/Quantitative Translation, in that order. Two parts of sample free-response Question 1 open by instructing students to begin the derivation by writing a fundamental physics principle or an equation from the reference information. On a Topic 3.4 question that means the answer starts from a conservation statement written down explicitly, then substitutes, rather than starting from a rearranged formula.

None of that changes what energy conservation is. It changes what a complete answer looks like.

Choosing the system is the whole topic

Learning objective 3.4.C is unusual: it is an objective about a modelling decision rather than about a physical quantity. Read its three statements as a procedure, because that is what they are.

3.4.C.1: energy is conserved in all interactions. Unconditional. There is no situation in this course where energy fails to be conserved. When people say energy "was lost," they mean it left the system they had drawn.

3.4.C.2: if the work done on a selected system is zero and there are no nonconservative interactions within the system, the total mechanical energy of the system is constant. Two conditions, both required. Zero external work, and no friction or drag inside the boundary.

3.4.C.3: if the work done on a selected system is nonzero, energy is transferred between the system and the environment.

Put together, the working procedure is:

Draw the boundary. Decide what is inside.
Check for external work. Any force from outside doing work on something inside means energy crosses the boundary, per 3.4.C.3.
Check for nonconservative interactions inside. Friction or drag inside the boundary means mechanical energy converts to something the course does not track.
If both checks come back clean, mechanical energy is constant and you may write $K_i + U_i = K_f + U_f$ .

Step 4 is a conclusion, not a starting assumption. Statement 3.4.B.3 is careful about this: a system may be selected so that the total energy of that system is constant. "May be selected" is permission, not a description of every system.

The practical consequence is that the same physical situation gives different bookkeeping depending on where you draw the line, and both are correct. A falling block on its own is a system with no potential energy at all, per 3.4.A.1, so gravity is an external force doing external work and 3.4.C.3 applies. Add Earth to the system and gravity becomes internal, gravitational potential energy exists, no external work is done, and 3.4.C.2 applies. The speed at the bottom comes out the same. Worked example 1 does it both ways and gets 5.94 m/s twice.

Statement 3.4.A.1 is the rule that makes the first of those two accounts work: a system composed of only a single object can only have kinetic energy. If you have written a potential energy term for a single-object system, the system boundary is wrong, not the algebra.

Balancing the books (3.4.B.1 to 3.4.B.4)

Objective 3.4.B is the arithmetic side of the same idea.

3.4.B.1 defines mechanical energy as the sum of a system's kinetic and potential energies. That definition is worth stating precisely because the boundary statement fences the course to mechanical energy specifically. Thermal energy and sound are not part of the sum.

3.4.B.2 is the balance sheet: any change to a type of energy within a system must be balanced by an equivalent change of other types of energies within the system or by a transfer of energy between the system and its surroundings. Both branches of that "or" are examinable, and the CED's sample questions use one each.

Sample multiple-choice question 8 is tagged to 3.4.B.2 and tests the second branch. A student lifts a ball straight upward at constant speed, and two energy bar diagrams show the gravitational potential energy of the ball-Earth system and the kinetic energy of the ball at an earlier and a later time. The kinetic energy bar is unchanged, because the speed is constant. The potential energy bar has grown. Students must pick the bar representing the change in mechanical energy of the ball-Earth system, and the published answer is the one showing a positive change equal to the potential energy gain. The point of the question is that the mechanical energy of that system went up, which is only possible because the student is outside the system and transferred energy in. That is 3.4.C.3 and 3.4.B.4 together.

Sample multiple-choice question 1 is tagged to the same statement and tests the first branch. A block is released from rest and slides down a track with negligible friction, descending 5.0 m to a point, then slides along a horizontal surface where the coefficient of kinetic friction is 0.20. Students are asked how far it slides before stopping, and the published answer is 25 m. Worked example 2 works the general version, in which the mass and $g$ both cancel and the answer is just the height divided by the coefficient.

3.4.B.4 closes the loop: if the total energy of a system changes, that change equals the energy transferred into or out of it. Combined with 3.4.C.3, that is the work-energy theorem written for a system rather than for an object.

On energy bar charts generally: skill 1.B, quantitative graphs with scales and plotted data, is one of this topic's suggested skills, and Science Practice 1 is not assessed on the multiple-choice section of the AP Physics C: Mechanics exam at all. It carries 20 to 35% of the free-response section. Bar charts and plotted graphs in Topic 3.4 point at the free-response paper.

Where the energy goes, and where the course stops

The boundary statement is one sentence: AP Physics C: Mechanics expects students to know that mechanical energy can be dissipated as thermal energy or sound by nonconservative forces.

Read it with Topic 3.2's boundary statement, because the two are halves of one fence and neither says the whole thing. Topic 3.2's reads that the course only expects students to analyze the transfer of mechanical energy, although students should be aware that mechanical energy may be dissipated in the form of thermal energy or sound.

Together: analysis stops at mechanical energy; awareness extends one step past it. You are expected to name thermal energy or sound as the destination of missing mechanical energy, and to attribute the loss to a nonconservative force. You are not expected to do anything thermodynamic with it. No temperature change, no specific heat, no entropy, no heat transfer. Those belong to AP Physics 2, and AP Physics 1's version of the Topic 3.2 boundary statement says so explicitly while the AP Physics C: Mechanics version drops the pointer, because there is no AP Physics C course that picks it up.

So on a free-response question where a block slides to a stop, a complete answer says the mechanical energy was dissipated as thermal energy and sound by the nonconservative friction force, quantifies it as the friction force times the path length per essential knowledge 3.2.A.4.iii, and stops there.

One wording trap. "Energy is conserved" and "mechanical energy is constant" are not the same claim. The first is 3.4.C.1 and is always true. The second is 3.4.C.2 and holds only under two conditions. A block sliding to a halt on a rough floor satisfies the first and violates the second. Writing "energy is not conserved because of friction" is a defect that the CED's own statements contradict directly.

The CED is also blunt about justification style. The Unit 6 Preparing for the AP Exam note states that simply referencing an equation, law, or physical principle is not sufficient, and that stating one object is faster than another because of "conservation of energy" is not a complete enough answer to earn credit on the free-response section: students must explain the steps in their reasoning that lead from the principle to the claim. Topic 3.4 is where that warning bites hardest, because "conservation of energy" is the phrase most available to write.

How Topic 3.4 is tested

Topic 3.4 is the most heavily sampled topic in the whole AP Physics C: Mechanics course and exam description, and objective 3.4.B is the reason.

	Sample multiple-choice	Sample free-response
3.4.A	none	none
3.4.B	Questions 1 and 8, both tagged to 3.4.B.2	Questions 1, 3 and 4
3.4.C	none	Question 3

Objective 3.4.B appears in three of the four sample free-response questions. No other objective in the course appears in three. It shows up in Question 1, the Mathematical Routines question built on a potential energy graph; in Question 3, the Experimental Design and Analysis question; and in Question 4, the Qualitative/Quantitative Translation question that races a hollow sphere, a uniform solid sphere and a hoop down a ramp.

Question 3 is worth a closer look, because it is the only sample question that reaches 3.4.C and because it is an energy question wearing lab clothes. Its first half gives two carts on a straight horizontal track, one moving and one at rest with a spring attached, and asks students to indicate what could be measured, and what to graph, to determine whether the initial speed changes the fraction of total kinetic energy remaining after the collision. Its second half puts a cart at the bottom of a ramp, has an impulse device deliver the same impulse to it in every trial with blocks of different known masses attached, tabulates the maximum vertical height reached against the combined mass, and asks students to choose axes that linearize the data, plot it, draw a best-fit line and extract the impulse. Both halves are the same physics: kinetic energy converting into something else, with the accounting decided by where the system boundary sits.

Objective 3.4.A appears in no sample question at all, which is consistent with its two statements being definitional rather than computational.

Unit 3's Progress Check is about 18 multiple-choice questions and four free-response questions, one of each type.

Related pages. The conservation of energy guide owns the step-by-step energy-accounting routine and the work-energy theorem guide owns the work-to-speed one; both were written for the constant-force regime the two courses share. Mechanical energy is the one-paragraph definition, conservative versus nonconservative force is the split that decides which of 3.4.C.2's two conditions you are checking, and work, energy and power practice has problems in the shared regime. The Unit 3 hub lists every equation in the unit against what the sheet prints.

The same block, two system choices, one answer

A 2.5 kg block is released from rest and slides 1.80 m down in height along a frictionless incline of 30 degrees. Take $g = 9.8\ \mathrm{m/s^2}$ . Find its speed at the bottom (a) treating the block alone as the system and (b) treating the block and Earth as the system. (c) Repeat part (b) with a coefficient of kinetic friction of 0.20 between block and incline.

Declare the convention: down the slope is the positive direction of motion, and $y$ increases upward with the bottom of the incline at $y = 0$ .
(a) System: the block alone. By 3.4.A.1 a single-object system can only have kinetic energy, so there is no potential energy term to write. Gravity is external, so 3.4.C.3 applies and energy crosses the boundary.
The work done by gravity is $W = mgh = (2.5)(9.8)(1.80) = 44.1$ J. The normal force is perpendicular to the motion and does none.
By the work-energy theorem, $\Delta K = 44.1$ J with $K_i = 0$ , so $v = \sqrt{2(44.1)/2.5} = \sqrt{35.28} = 5.9397$ m/s, or 5.94 m/s.
(b) System: block plus Earth. Gravity is now internal and conservative, no external force does work, and there is no friction inside the boundary, so both conditions of 3.4.C.2 are met and the total mechanical energy is constant.
$K_i + U_i = K_f + U_f$ with $K_i = 0$ and, taking $U_f = 0$ at the bottom per 3.3.A.3, $U_i = mgh = 44.1$ J.
So $K_f = 44.1$ J and $v = \sqrt{35.28} = 5.94$ m/s, the same number. The 44.1 J that was external work in (a) is internal potential energy in (b). Nothing physical changed; the boundary moved.
(c) With friction. The distance along the incline is $d = h/\sin 30^\circ = 1.80/0.500 = 3.60$ m.
The normal force is $F_N = mg\cos 30^\circ = (2.5)(9.8)(0.8660) = 21.218$ N, using $\cos 30^\circ = \sqrt{3}/2$ from the trigonometric table printed in the Table of Information.
The friction force is $F_f = \mu_k F_N = (0.20)(21.218) = 4.2435$ N, and by 3.2.A.4.iii the energy dissipated is $F_f d = (4.2435)(3.60) = 15.277$ J.
Now the second condition of 3.4.C.2 fails: there is a nonconservative interaction inside the system. Mechanical energy is not constant. $K_f = 44.1 - 15.277 = 28.823$ J.
$v = \sqrt{2(28.823)/2.5} = \sqrt{23.059} = 4.8019$ m/s, or 4.80 m/s.
State the destination, per the boundary statement: the missing 15.3 J was dissipated as thermal energy and sound by the nonconservative friction force. Energy is still conserved (3.4.C.1); the system's mechanical energy is not constant.

(a) and (b) both give 5.94 m/s. Treating the block alone makes gravity an external force doing 44.1 J of work; adding Earth makes the same 44.1 J an internal potential energy. (c) With friction the speed is 4.80 m/s, because 15.3 J of the 44.1 J was dissipated as thermal energy and sound.

Why the stopping distance does not depend on mass or on g

A block is released from rest and slides down a frictionless track, descending a vertical height $h$ , then continues onto a rough horizontal surface with coefficient of kinetic friction $\mu_k$ . Derive an expression for the distance $d$ it slides before stopping, then evaluate it for $h = 2.4$ m and $\mu_k = 0.32$ .

Choose the system as block plus Earth plus surface, so gravity and friction are both internal and no external force does work on it.
On the descent, 3.4.C.2's conditions hold (the track is frictionless), so the mechanical energy is constant and the kinetic energy at the bottom is $K = mgh$ , using $\Delta U_g = mg\Delta y$ from 3.3.A.7.iii.
On the horizontal stretch the friction interaction is nonconservative, so mechanical energy is dissipated. The normal force on a horizontal surface is $F_N = mg$ , so the friction force is $\mu_k mg$ .
Per 3.2.A.4.iii, the energy dissipated over a path of length $d$ is $\mu_k mg\, d$ . The block stops when all of the kinetic energy is gone.
Set them equal: $mgh = \mu_k mg\, d$ .
Both $m$ and $g$ appear on each side and cancel: $d = \dfrac{h}{\mu_k}$ .
That is the whole result, and it is worth pausing on. The stopping distance depends only on the drop height and the coefficient of friction. A heavier block gains more kinetic energy and also experiences proportionally more friction, and the two effects cancel exactly.
It also means the value of $g$ never enters. A Topic 1.3 boundary statement says the AP Physics C courses expect $g \approx 10\ \mathrm{m/s^2}$ where a numerical value is needed while not penalising 9.81 or 9.8, and on this problem the choice makes no difference at all.
Evaluate: $d = 2.4/0.32 = 7.5$ m.
Check against the CED's own version. Sample multiple-choice question 1 gives a 5.0 m drop and $\mu_k = 0.20$ , and the published answer is 25 m. Our expression gives $5.0/0.20 = 25$ m.

$d = h/\mu_k$ , independent of both the mass and the value of $g$ . For $h = 2.4$ m and $\mu_k = 0.32$ , the block slides 7.5 m.

Lifting at constant speed: nothing changes, and something does

A student lifts a 4.0 kg box straight upward at a constant speed through a height of 1.5 m. Take $g = 9.8\ \mathrm{m/s^2}$ . For (a) the box alone as the system and (b) the box and Earth as the system, state the change in kinetic energy, the change in potential energy, the change in mechanical energy, and the work done on the system from outside.

Set the convention: upward is positive, and the speed is constant so $v_i = v_f$ .
(a) System: the box alone. By 3.4.A.1 this system has only kinetic energy, so $\Delta U = 0$ by definition, not by cancellation.
The speed is constant, so $\Delta K = 0$ and therefore $\Delta E_{\text{mech}} = 0$ .
Two external forces do work on it. The student's applied force does $+mgh = (4.0)(9.8)(1.5) = +58.8$ J, and gravity does $-58.8$ J. The net external work is zero, consistent with $\Delta K = 0$ and the work-energy theorem.
(b) System: box plus Earth. Gravity is now internal, so it no longer appears as external work. $\Delta K$ is still 0.
$\Delta U_g = mg\Delta y = (4.0)(9.8)(1.5) = +58.8$ J, per 3.3.A.7.iii.
$\Delta E_{\text{mech}} = \Delta K + \Delta U = 0 + 58.8 = +58.8$ J. The mechanical energy of this system increased.
That is only allowed because the student is outside the boundary. The external work done on the system is $+58.8$ J, which matches the change exactly, which is 3.4.B.4 and 3.4.C.3.
Compare the two accounts in a line. System (a): mechanical energy unchanged, external work zero. System (b): mechanical energy up by 58.8 J, external work up by 58.8 J. Both obey 3.4.B.2, and neither violates 3.4.C.1, because nothing was created.
This is the structure of the CED's sample multiple-choice question 8, which shows the same situation as two energy bar diagrams and asks for the change in mechanical energy of the ball-Earth system. The kinetic energy bar is unchanged and the potential energy bar has grown, so the change is positive and equals the potential energy gain.
The trap in that question is answering zero, on the reasoning that constant speed means nothing changed. Constant speed means $\Delta K = 0$ . It says nothing about $\Delta U$ .

(a) Box alone: $\Delta K = 0$ , no potential energy term exists, $\Delta E_{\text{mech}} = 0$ , and the net external work is zero (the student does $+58.8$ J and gravity does $-58.8$ J). (b) Box plus Earth: $\Delta K = 0$ , $\Delta U_g = +58.8$ J, $\Delta E_{\text{mech}} = +58.8$ J, matched by $+58.8$ J of external work from the student.

Frequently asked questions

Is AP Physics C Topic 3.4 different from AP Physics 1 Topic 3.4?

The required content is identical. All three learning objectives and all nine essential knowledge statements are word for word the same in both course and exam descriptions, in the same order under the same numbers, and neither course adds a sub-statement. The boundary statements differ only in the course name. What differs is around the content: the suggested skills swap qualitative diagrams for quantitative graphs and add creating experimental procedures, the calculus-based course allows about 12 to 17 class periods for the whole unit against 22 to 27, and its free-response questions expect derivations that begin from a stated principle and end in a symbolic answer.

How do you choose a system in an AP Physics C energy problem?

Draw a boundary, then check two things. Essential knowledge 3.4.C.2 says that if the work done on the selected system is zero and there are no nonconservative interactions within it, the total mechanical energy of that system is constant. So check whether any outside force does work on anything inside, and check whether friction or drag acts inside the boundary. If both come back clean you may set the initial mechanical energy equal to the final. If external work is nonzero, 3.4.C.3 says energy is transferred between the system and the environment, and you account for it as work. The same situation can be analysed with different boundaries and will give the same physical answer.

Does a falling object have potential energy in AP Physics C?

Only if Earth is inside the system you chose. Essential knowledge 3.4.A.1 states that a system composed of only a single object can only have kinetic energy, so a system consisting of just the falling object has no potential energy term at all, and gravity acts on it as an external force doing external work. Put the object and Earth in the system together and gravity becomes an internal conservative interaction, gravitational potential energy exists, and no external work is done. Both analyses give the same final speed. Writing a potential energy for a single-object system means the boundary, not the algebra, is wrong.

Is energy conserved when there is friction?

Yes. Essential knowledge 3.4.C.1 states without qualification that energy is conserved in all interactions. What friction breaks is the narrower claim in 3.4.C.2, that the total mechanical energy of a selected system is constant, since that requires no nonconservative interactions inside the boundary. Saying that energy is not conserved because of friction contradicts the CED directly. The correct statement is that mechanical energy was dissipated, and the Topic 3.4 boundary statement says where to: mechanical energy can be dissipated as thermal energy or sound by nonconservative forces.

How much of AP Physics C Mechanics is conservation of energy?

Unit 3 as a whole is weighted 15 to 25% of the multiple-choice section, at about 12 to 17 class periods, and Topic 3.4 is the part of it the CED samples most. Learning objective 3.4.B appears in three of the four sample free-response questions, more than any other objective in the course, and in two of the fifteen sample multiple-choice questions, both tagged to essential knowledge 3.4.B.2. Objective 3.4.C appears in one sample free-response question and objective 3.4.A in none. Topic 3.4 is also the only topic in Unit 3 carrying three learning objectives; the other four carry one each.

Does AP Physics C Mechanics cover thermal energy or entropy?

No. Two boundary statements draw the line. The one under Topic 3.4 says the course expects students to know that mechanical energy can be dissipated as thermal energy or sound by nonconservative forces. The one under Topic 3.2 says the course only expects students to analyze the transfer of mechanical energy, although students should be aware that mechanical energy may be dissipated in the form of thermal energy or sound. Together they mean you name thermal energy or sound as the destination of missing mechanical energy and attribute the loss to a nonconservative force, and go no further. There is no temperature change, no specific heat, no heat transfer and no entropy anywhere in the course.